is a parallelogram with , and . If the area of the parallelogram is , what is the value of ?Source: NCTM Mathematics Teacher, November 2006

SOLUTIONDraw a perpendicular to . If the x-coordinate of equals , its y-coordinate equals because has a slope of .
Use distance formula to calculate
Area of
Since is perpendicular to , its slope equals
Use distance formula to calculate
Squaring both sides
Substitute the value of from Eq.
Substitute the value of into Eq.

Answer:

Alternative solution
We can find the coordinates of by adding the x-coordinate of and and the y-coordinates of and
Area of =area of rectangle -area of the four triangles , and